Having established that permutation equivariance is a desirable property for UWMMSE and guided by Proposition REF , we proceed to specify a particular \(\Psi \) . Inspired by the simplicity of graph convolutional networks in [1]}, we propose the following function
\(\Psi ({\mathbf {H}}; \theta ) & = \alpha _2 \left( \mathrm {diag}({\mathbf {H}}) \, {\mathbf {Z}}\, \omega _{21} + {\mathbf {H}}\, {\mathbf {Z}}\,\omega _{22} \right), \\{\mathbf {Z}}& = \alpha _1 \left( \mathrm {diag}({\mathbf {H}}) \, \mathbf {1} \, \omega ^\top _{11} + {\mathbf {H}}\, \mathbf {1} \,\omega ^\top _{12} \right), \) 
